My speedometer was getting twitchy so I disconnected both ends
and slid out the core. It all appears good to me, no kinks or
obvious abnormalities.
What kind of grease is best to use on the core when I put it
back in ? Does the kind of grease make much difference ?

I wouldn't think it'd be a dealbreaker but your parts house will have a small tube of speedo cable specific grease

Powdered graphite is the ticket...

Graphite is what I've used.

If you read the internet many also say white lithium type grease works too.

What you don't want is any sort of oil. When it gets cold the oil viscosity will change enough to make the cable hang up and cause the needle to fluctuate. It goes away when the car gets warmed up, but still annoying.

Thank you, Gents.
Right now there is some kind of lube on the core, not much
though. Kind of greasy feeling.
Graphite sounds best.

Are they lubed new as spare part? I installed mine (NOS), haven't driven the car yet, but I did not pull out the cable to see before putting in place. Making me wonder now if I should have "enhanced" before installing.

Cable lube.

[s][/s]

Is the that "cable lube" a grease or powder?

It's a liquid graphite.